A -functional and the rate of convergence of some linear polynomial operators

We show that the -functional

where , is equivalent to the rate of convergence of a certain linear polynomial operator. This operator stems from a Riesz-type summability process of expansion by Legendre polynomials. We use the operator above to obtain a linear polynomial approximation operator with a rate comparable to that of the best polynomial approximation.

     

选相原位法合成立方氮化硼的关键影响因素

利用选相原位法在水溶液中成功制备出了立方氮化硼晶体，对反应条件进行了优化。结果表明，利用选相原位法合成立方氮化硼的最佳实验条件是：反应压力为10.0 MPa，在氯离子加入下利用混合氮源进行反应。在该条件下得到了纯相的立方氮化硼晶体。     

不同光滑度立方体氧化铁对液晶电光性能的改善

向列相液晶被广泛应用于液晶显示中,但是由于杂质的存在,会导致液晶的驱动电压变大,增加能耗。 为了降低阈值电压和饱和电压,通常向液晶中添加纳米颗粒来提高电光性能。 本文利用水热法制备了表面粗糙和光滑的两种立方体Fe₂O₃纳米颗粒,其形貌均匀,尺寸约550 nm。 将二者分别掺杂到向列相液晶E7中,结果表明,粗糙立方体Fe₂O₃/E7复合体系具有比光滑立方体Fe₂O₃/E7复合体系和向列相液晶E7更优的电光性能,且在掺杂质量分数为0.4%时,其电光性能达到最优,阈值电压和饱和电压分别降低9.9%和11.6%,对比度增大80%,响应时间降低至6.0 ms。 这归因于粗糙立方体Fe₂O₃具有足够的表面积和表面所带电荷更多,所以会更易吸附体系中的杂质离子和减弱杂质离子的屏蔽作用,从而提高了电光性能。     

鞘磷脂和神经节苷脂对磷脂酰乙醇胺混合脂超分子体系液晶态立方相Im3m和Pn3m结构影响的研究

用磷脂酰乙醇胺(DEPE)、鞘磷脂(Sphingomyeline, Sph)、神经节苷脂(Gm1)和胆固醇(Chol)模拟了生物膜超分子体系液晶态结构, 通过用小角X射线衍射(SAXD)对混合脂体系液晶态结构进行了研究, 鉴定出了两种立方相: 即Im3m(Q²²⁹)和Pn3m(Q²²⁴)结构. 实验发现, 鞘磷脂的含量对DEPE膜的结构有一定的影响, 随着鞘磷脂浓度的增加, 混合脂体系的液晶态结构发生了由Im3m(Q²²⁹)到Pn3m(Q²²⁴)的变化. 神经节苷脂(Gm1)的含量对混合脂体系的液晶态结构也有一定的影响, 当神经节苷脂(Gm1)含量达到某一临界值时, 混合脂体系的液晶态结构发生了从Im3m(Q²²⁹)到Pn3m(Q²²⁴) 的变化. 当DEPE-Shp-Gm1超分子聚集体中含有胆固醇时, 胆固醇的极性头部(—OH)与磷脂酰乙醇胺(DEPE)、鞘磷脂(Shp)、神经节苷脂(Gm1)的极性头部通过氢键相互作用形成液晶态立方相Im3m(Q²²⁹)结构, 再通过疏水/亲水相互作用形成稳定的Pn3m (Q²²⁴)结构.     

Improving the rate of convergence of interior point methods for linear programming

This paper proposes a procedure for improving the rate of convergence of interior point methods for linear programming. If (x ^k ) is the sequence generated by an interior point method, the procedure derives an auxiliary sequence ( ). Under the suitable assumptions it is shown that the sequence ( ) converges superlinearly faster to the solution than (x ^k ). Application of the procedure to the projective and afflne scaling algorithms is discussed and some computational illustration is provided.     

Functional Janus dendrimers containing carbazole with liquid crystalline,optical and electrochemical properties

ABSTRACT

Novel liquid crystalline Janus dendrimers that combine a mesogenic block and an electroactive block have been synthesised. The mesogenic block is based on two third-generation Percec-type dendrons bearing six or eight terminal dodecyloxy alkyl chains, whereas the electroactive blocks are formed by one or two carbazole units. The liquid crystal behaviour was investigated by polarised-light optical microscopy, differential scanning microscopy and X-ray diffraction. The Janus dendrimers with one electroactive unit exhibited cubic or columnar liquid crystal phases, whereas the Janus dendrimers with two electroactive units did not show liquid crystalline behaviour. The UV-vis absorption and emission properties of the Janus dendrimers were investigated. The spectra suggested the existence of π-π stacking and the formation of aggregates in the solid state. Electrodeposition of the carbazole-containing dendrimers afforded semi-globular particles in which the number of electropolymerizable units and the flexible or rigid character of the linker have a decisive influence in the particle size.     

The a posteriori error estimates of Chebyshev–Petrov–Galerkin methods for second-order equations

In this paper, the a posteriori error estimates of Chebyshev–Petrov–Galerkin approximations are investigated. For simplicity, we choose the Poisson equation with Dirichlet boundary conditions to discuss the a posteriori error estimators, and deduce their efficient and reliable properties. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error estimators.     

Metastable ionic cubic structure I clathrate hydrate formed with tetra-n-butylammonium bromide

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